1. Field of the Invention
This invention relates to apparatus and method for determining characteristics of a mechanical system, and more particularly to such apparatus and methods for determining kinetic energy, potential energy and dissipation functions for a single degree of freedom machine.
2. Description of the Prior Art
The general form of a nonlinear differential equation governing the motion of any single degree of freedom holonomic system is known. The characteristics of a scleronomic holonomic system are defined in the text entitled Dynamics, authored by Thomas R. Kane, published by Holt, Rinehart, and Winston, Inc., copyright 1968, pages 13-15. Given certain information regarding the mechanical system, other system information may be found. Given system parameters and desired response, the required input to the system may be determined. Given system input and desired response, required system parameters may be determined. Given system parameters and input, resulting response may be determined. If the system input and response are measured, system parameters may be determined.
The utility of the last mentioned approach, identification of system parameters, has only recently been recognized. In U.S. patent application Ser. No. 413,926, filed Sept. 1, 1982 now U.S. Pat. No. 4,457,165 and assigned to the Assignee of the instant application, it was disclosed that determination of kinetic energy, potential energy and dissipation functions relative to a particular mechanical system formed the basis for dynamic analysis of the system. When the response of a single degree of freedom machine is observed while being driven by a forced periodic input torque, information is obtained whereby the aforementioned functions may be determined. It was therein stated that such determinations may be utilized in applications relating to machinery development, quality control and machine diagnosis. This disclosure was limited by the requirement of effecting solutions in the frequency domain and therefore by a requirement that machine shaft excitation be in the form of a known oscillatory steady state quantity.
A recent work relates to experimentally improving the balancing of a mechanism through a form of mechanism identification. Tricamo, S. J., and Lowen, G. G., "A New Concept For Force Balancing Machines For Planar Linkages, Part I: Theory; Part II: Application to Four-Bar Linkage and Experiment", ASME Journal of Mechanical Design, Volume 103, No. 3, July 1981, pages 637-642 and Volume 103, No. 4, October 1981, pages 784-792, respectively. In this work it was found that crankshaft speed variations could not be ignored. A theory for identification of sources of kinematic errors in planar mechanisms was presented by Dubowsky, S., Maatuk, J., and Perreira, N. D., "A Parameter Identification Study Of Kinematic Errors In Planar Mechanisms", ASME Journal of Engineering For Industry, Volume 97, No. 2, May 1975, pages 635-642.